Bulk locality from the celestial amplitude

Chi-Ming Chang Yau Mathematical Sciences Center (YMSC), Tsinghua University, Beijing, 100084, China; Beijing Institute of Mathematical Sciences and Applications (BIMSA), Beijing, 101408, China Yu-tin Huang Department of Physics and Center for Theoretical Physics, National Taiwan University, Taipei, Taiwan 106; Physics Division, National Center for Theoretical Sciences, Taipei 10617, Taiwan Zi-Xun Huang Department of Physics and Center for Theoretical Physics, National Taiwan University, Taipei, Taiwan 106 Wei Li Department of Physics and Center for Theoretical Physics, National Taiwan University, Taipei, Taiwan 106

arXiv subject: High Energy Physics - Theory (hep-th) mathscidoc:2207.74022

SciPost Physics, 12, (176), 2022.5
In this paper, we study the implications of bulk locality on the celestial amplitude. In the context of the four-point amplitude, the fact that the bulk S-matrix factorizes locally in poles of Mandelstam variables is reflected in the imaginary part of the celestial amplitude. In particular, on the real axis in the complex plane of the boost weight, the imaginary part of the celestial amplitude can be given as a positive expansion on the Poincar\'e partial waves, which are nothing but the projection of flat-space spinning polynomials onto the celestial sphere. Furthermore, we derive the celestial dispersion relation, which relates the imaginary part to the residue of the celestial amplitude for negative even integer boost weight. The latter is precisely the projection of low energy EFT coefficients onto the celestial sphere. We demonstrate these properties explicitly on the open and closed string celestial amplitudes. Finally, we give an explicit expansion of the Poincar\'e partial waves in terms of 2D conformal partial waves.
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@inproceedings{chi-ming2022bulk,
  title={Bulk locality from the celestial amplitude},
  author={Chi-Ming Chang, Yu-tin Huang, Zi-Xun Huang, and Wei Li},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220702144312963336518},
  booktitle={SciPost Physics},
  volume={12},
  number={176},
  year={2022},
}
Chi-Ming Chang, Yu-tin Huang, Zi-Xun Huang, and Wei Li. Bulk locality from the celestial amplitude. 2022. Vol. 12. In SciPost Physics. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220702144312963336518.
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